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Undergraduate Research Opportunities

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Department of Mathematics students conduct significant research in an in-house SOAR program and in Research Experiences for Undergraduates (REU) programs across the country. Our students present findings in poster sessions at the joint national meeting for the Math Association of America (MAA) and the American Mathematical Society (AMS) each January at a new venue each year.

Student Opportunities in Accelerated Research (SOAR) Program

Established in 2008, the SOAR Program is an opportunity for students in the Department of Mathematics at Grove City College to participate in a short-term, focused research project. For four weeks each summer the College invites three math students to work on a research project. The SOAR Program is generously funded by Grove City College's Swezey Fund for Scientific Research and Instrumentation. The Department of Mathematics continues the SOAR Program based upon adequate levels of support.

Polytope Numbers

Over the last six years, the SOAR Program has been investigating polytope numbers which are number sequences created from the geometry of polytopes.

Building on the work of H.K. Kim of Pohang University in Korea, student researchers in the SOAR Program have found various formulae for polytope number sequences. Work has included investigating polytope number sequences for polytopes created by various operations such as rectification (cutting off each vertex to the middle of the adjacent edges), r-rectification (cutting off each vertex to the middles of each adjacent r-facet), as well as expansion (replacing each edge by a square face and adding other edges and vertices are necessary). In many cases, our students were able to write these polytope number sequences as linear combinations of simplex number sequences, and to generalize the work of polytope number sequences to non-spherical polytopes in both dimensions 3 and 4.

During the summer of 2013, the SOAR Program developed a method to step up to compute polytope number sequences in order to extend work beyond where H.K. Kim’s process could be initially applied. The SOAR Program continues in its efforts to modify the stepping up process to work in more situations.

Research Experiences for Undergraduates (REU) Programs

Our students have participated in REU programs across the country including:

  • “Current Research on HONB-Zipfian Correlations” Zach Wheeler, Rutgers University, Summer 2014
  • “Modeling Illicit Drug Use: Methamphetamine” Robin Mabe, North Carolina State University, Summer 2013
  • “Classifying Extensions of the Field of Formal Laurent Series Over” Dan Scofield, Clemson University, Summer 2012
  • “Pebbling on Graphs” Mark Schrecengost, Hope College, Summer 2012
  • “Expander Families of Graphs” Brad Weaver, Kent State University, Summer 2011
  • “Minkowski Length of a Polyhedra” Brad Weaver, Kent State University, Summer 2010
  • “Taking Curvature to the Extreme!” Lindsay Willett, Hope College, Summer 2009
  • “The Martian Program: Modeling the Development of Sensorimotor Intelligence in Infants” Andrew Falcone, University of Idaho, Summer 2009
  • “Bernoulli Convolutions: A Combinatorial Approach” Julia Davis, Clemson University, Summer 2008
  • “Computational Ramsey Theory” Tim Hopper, Rochester Institute of Technology, Summer 2007
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